Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
526 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17986367 | C2 | semidirect |
| 4. C2×#17985740 | C2 | semidirect |
| 6. #22586221 | C2 | semidirect |
| 7. C71×#1993 | C2 | semidirect |
| 192. #1993 | D71 | semidirect |
| 196. C71 | #10083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986367 | 2 |
| C2×#17986361 | 2 |
| #22596392 | 2 |
| C2×#17985740 | 2 |
| C2×#17985738 | 2 |
| #22586221 | 2 |
| C71×#1993 | 2 |
| #10083 | 71 |